It seems to me at least that a conventionally organized army's command structure would go against their beliefs, though it also doesn't seem possible to me that an army could be organized without some form of leadership, so how was it run?
In the Black Army, officers were mostly democratically elected and recallable (though some were appointed directly by the 'higher ups'), and decisions were often made in general assemblies and elected councils. Unlike many other armies of the time, the officers consisted mostly of peasants. Keep in mind that this was not the ideal, utopian organization of the anarchists, but one made out of necessity in response to their circumstances. It was imperfect, but did strive to have leadership structures for logistical purposes without socially and economically stratified forces.
(see Paul Avrich, Anarchist Portraits, 114-115, also https://en.wikipedia.org/wiki/Revolutionary_Insurrectionary_Army_of_Ukraine#Organisation )
If it was like Spain at all, the pay/rations were mostly even across ranks as well, as rank was for organization but not status. There's a few books on Makhno's anarchist forces, but there's a lot more on anarchism in the Spanish Civil War.